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Show that 5 − 2 √ 3 is an Irrational Number. - Mathematics

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Question

Show that \[5 - 2\sqrt{3}\] is an irrational number.

Numerical

Solution

Let us assume that `5-2sqrt3` is rational .Then, there exist positive co primes a and b such that

\[5 - 2\sqrt{3}\] `=a/b`
`2sqrt3=a/b-5`
`sqrt3=((a/b)-5)/2`
`sqrt3= (a-5b)/(2b)`
This contradicts the fact that `sqrt3` is an irrational 
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Chapter 1: Real Numbers - Exercise 1.5 [Page 49]

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RD Sharma Mathematics [English] Class 10
Chapter 1 Real Numbers
Exercise 1.5 | Q 6 | Page 49

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